Move modifier to the top of the stack through python
This can be done by some simple scripting. I assume obj is filled with the object with the modifier stack

def modifiers_by_name(obj, name):
    """ Find all modifiers with a specific name in obj """
    return [x for x in obj.modifiers if x.name == name]

def modifiers_by_type(obj, typename):
    """ Find all modifiers with a specific type in obj """
    return [x for x in obj.modifiers if x.type == typename]

# move all "Screw" modifiers to the top
for modifier in reversed(modifiers_by_type(obj, "SCREW")):
    # while modifier not on top
    while obj.modifiers.find(modifier.name) != 0:
        # move it one more to the top.
        bpy.ops.object.modifier_move_up(modifier=modifier.name)


Note I reversed the modifiers so the top "Screw" modifier will still be on the top after execution